A matrix, H, arising in multiple regression, which is used to obtain the predicted values of the response variable corresponding to each observed value via the equation
ŷ = Hy
The matrix H puts the ‘hats’ on the elements of y; it is a symmetric matrix and is also idempotent.
Given explicitly in terms of design matrix, X as
𝐻 = 𝑋(𝑋’𝑋)−1𝑋
The diagonal elements of H are often useful diagnostically in assessing the results from the analysis.